Lecture 10
Overview
 A Futures Contract on an Option
◦ The underlying asset is not a stock
◦ The underlying asset is a futures contract
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Call Futures Option
◦ Long Call = The right to long a futures contract
◦ Short Call = The obligation to short a futures
contract
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Put Futures Option
◦ Long Put = The right to short a futures contract
◦ Short Put = The obligation to long a futures
contract
Option Specifications
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Futures Options = FO
No delivery occurs
Commodities are Settled in Cash
Financials might take delivery
One option = one futures contract
Expiration
◦ Financial options
 Same date as futures contract expiration
◦ Commodity Options
 Expire the month prior to the futures contract expiration
Pricing
 FO prices are listed in “units”
 Each “Unit” has a $ value
Example (Corn FO)
 Underlying asset = 5,000 bushels of corn
 1 unit = $6.25 (or 1/8 cents per bushel)
 Dec300Call = 80
◦ 80 x $6.25 = $500
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The strike of 300 = $3.00 or 300 cents per
bushel
CBOT lists details
Example (Soybean FO)
 March soybean futures are selling for 575 cents per
bushel
 The underlying asset is one futures contract on 5,000
bushels of soybeans as listed on the CBOT
 The value of one futures contract
◦ 5000 x $5.75 = $28,750
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The unit value is $50
◦ Determined 5000 x .01 = $50
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The futures option price is quoted in Units (which
are cents per bushel)
But the total price is $50 x cents
Example (Soybean FO) - continued
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Mar525P = 5
Mar550C = 35.50
Mar600C = 8.25
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BE on March550C = 550 + 35.50 = 585.50
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(total cost = $50 x 5 = $250)
($1,775)
($ 412.50)
Units
 Vary depending on the underlying asset
 Each asset has a unique relationship among
◦ Asset price
◦ Futures Contract specs
◦ Option
Basic Underlying Asset Categories
 Commodity
 Financial
 Currency
 others
Example - gold is quoted in $ per ounce
Example - Sugar is quoted in cents per pound
CBOT web site
Pricing – Same as regular options.
Black Scholes
Binomial
FO Margin
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Determined by volatility and risk of loss
Futures Options use unique margin accounting
SPAN= Standard Portfolio ANalysis of Risk
Futures Options Uses
Same as futures w/ flexibility
Floors, ceilings, spreads, etc
Employs all Option strategies
Arbitrage (lots of mispricing)
Birth 1981
Definition - An agreement between two firms, in which each firm
agrees to exchange the “interest rate characteristics” of two
different financial instruments of identical principal
Key points
Spread inefficiencies
Same notation principal
Only interest exchanged
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“Plain Vanilla Swap” - (generic swap)
fixed rate payer
floating rate payer
counterparties
settlement date
trade date
effective date
terms
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Swap Gain = fixed spread - floating spread
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Example (vanilla/annually settled)
XYZ
ABC
fixed rate
10%
11.5%
floating rate
libor + .25
libor + .50
Q: if libor = 7%, what swap can be made 7 what is the profit (assume
$1mil face value loans)
A:
XYZ borrows $1mil @ 10% fixed
ABC borrows $1mil @ 7.5% floating
XYZ pays floating @ 7.25%
ABC pays fixed @ 10.50%
Example - cont
Benefit to XYZ
floating
+7.25
-7.25
fixed
+10.50 -10.00
Net gain
Net position
0
+.50
+.50%
Benefit ABC
floating
fixed
net gain
Net Position
-.25
+1.00
+.75%
+7.25
- 7.50
-10.50 + 11.50
Example - cont
Settlement date
ABC pmt 10.50 x 1mil
XYZ pmt 7.25 x 1mil
net cash pmt by ABC
= 105,000
= 72,500
= 32,500
if libor rises to 9%
settlement date
ABC pmt 10.50 x 1mil
XYZ pmt 9.25 x 1mil
net cash pmt by ABC
= 105,000
= 92,500
= 12,500
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transactions
rarely done direct
banks = middleman
bank profit = part of “swap gain”
example - same continued
XYZ & ABC go to bank separately
XYZ term = SWAP floating @ libor + .25 for fixed @ 10.50
ABC terms = swap floating libor + .25 for fixed 10.75
Example - cont
settlement date - XYZ
Bank pmt 10.50 x 1mil = 105,000
XYZ pmt 7.25 x 1mil
= 72,500
net Bank pmt to XYZ
= 32,500
settlement date - ABC
Bank pmt 7.25 x 1mil
ABC pmt 10.75 x 1mil
net ABC pmt to bank
= 72,500
= 107,500
= 35,000
bank “swap gain” = +35,000 - 32,500 = +2,500
Example - cont
benefit to XYZ
floating
7.25 - 7.25 =
0
fixed
10.50 - 10.00 = +.50
net gain .50
benefit to ABC
floating
fixed
net gain .50
7.25
- 7.50 = - .25
-10.75 + 11.50 = + .75
benefit to bank
floating
+7.25 - 7.25 =
0
fixed
10.75 - 10.50 = +.25
total benefit = 12,500 (same as w/o bank)
net gain +.25
Similar to interest rate swaps
Same type loan, just diff currency
WHY?
example:
you have an investment in Japan
Project is financed with US bonds
You look for SWAP partner so you can emulate holding Japanese
bonds
Yen loan
$ loan
Java
11%
8%
Yahoo
12%
11.1%
principal
$ 1 mil
or Y120
example - continued
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Java borrows $1mil @ 8%
Yahoo borrows Y120mil @ 12%
Intl. Bank arranges swap
Java swaps 8% $ loan for 10.3% yen loan w/bank
Yahoo swaps 12% yen loan for 10.4% $ loan w/bank
total available benefit = (11.1-8) - (12-11) = 2.1%
example - continued
benefit to Java
$ loan
+8 - 8 = 0
Yen loan
+11 - 10.3 = .7
net gain = +.7%
benefit to Yahoo
$ loan
11.1 - 10.4 = +.7
yen loan
-12 + 12 = 0
net gain = + .7%
benefit to bank
$ loan
+10.4 - 8 = +2.4
yen loan
- 12 + 10.3 = -1.7
net gain = + .7%